When a light ray centers a refracing medium, it is found that the magnitude of the angle of refraction is equal to half the angle of reflection. If `mu` is the refractive index of the medium, then the angle of incidence is

Options

A. `2sin^(-1)((mu)/(2))`
B. `2cos^(-1)((mu)/(2))`
C. `cos^(-1)((mu)/(2))`
D. `sin^(-1)((mu)/(2))`

Answer

B

Explanation

According to given problem,
Angle of refraction = `(1)/(2)` (Angle of reflection)
or `r.=(1)/(2)r`
As `mu=(sini)/(sinr)` (where i is the angle of incidence)
`mu=(sinr)/(sin((1)/(2)r))( :. "Angle of incidence", i= "Angle of refraction", r)`
`mu=(sinr)/(sin((1)/(2)r))( :. "Angle of incidence", i= "Angle of refraction", r)`
`cos^(-1)((mu)/(2))=(r)/(2)` or `r=2cos^(-1)((mu)/(2))`
`:.i=r :.i=2cos^(-1)((mu)/(2))`